We keep tossing a fair coin n=106 million times, write down the outcomes: it gives a...

We keep tossing a fair coin n=106 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i,i + 1,i + 2,i + 3,...,i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers i. What is the expected value of X? and calculate the numerical value. Could someone explain easily manner, please?

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orchestra answered 1 year ago

We keep tossing a fair coin n = 106 million times, write down the outcomes: it...

We keep tossing a fair coin n = 106 million times, write down the outcomes: it gives a Heads-and-Tails-sequence of length n. We call an integer i special, if the i, i + 1, i + 2, i + 3, . . . , i + 18-th elements of the sequence are all Heads. That is, we have a block of 19 consecutive Heads starting with the i-th element of the sequence. Let X denote the number of special integers...

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